Carnot Cycle Lab
Ideal heat engine
Live thermodynamic diagrams
Engine efficiency comparison
The Carnot engine sets the maximum theoretical efficiency for engines operating between the same hot and cold reservoir temperatures.
The physics
Ideal gas: pV = nRT, with R = 8.314 J/(mol K).
Carnot net work: W = nR(Tₕ − T꜀) ln(V₂/V₁).
Carnot efficiency: η꜀ = 1 − T꜀/Tₕ.
Carnot heat input: Qₕ = nRTₕ ln(V₂/V₁).
Otto-like efficiency: ηₒ = 1 − r^(1 − γ); γ = 1.4.
Otto-like constant-volume heating/cooling: Q = nCᵥΔT; Cᵥ = R/(γ − 1).
On a P–V diagram, net work equals the signed enclosed area ∮p dV. On a T–S diagram, reversible heat transfer equals ∫T dS.
Model: reversible ideal-gas cycles, fixed heat capacities, constant γ = 1.4. Volumes are in L on plots and converted to m³ for calculations. Pressures are in kPa. Carnot adiabats use TV^(γ−1) = constant. An Otto-like cycle has idealised isochoric heat transfer and adiabatic compression/expansion, with its minimum and maximum temperatures equal to T꜀ and Tₕ.